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Titlebook: Algebras of Linear Transformations; Douglas R. Farenick Textbook 2001 Springer Science+Business Media New York 2001 Multilinear Algebra.al

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發(fā)表于 2025-3-21 19:45:25 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
期刊全稱Algebras of Linear Transformations
影響因子2023Douglas R. Farenick
視頻videohttp://file.papertrans.cn/153/152792/152792.mp4
學(xué)科分類Universitext
圖書封面Titlebook: Algebras of Linear Transformations;  Douglas R. Farenick Textbook 2001 Springer Science+Business Media New York 2001 Multilinear Algebra.al
影響因子The aim of this book is twofold: (i) to give an exposition of the basic theory of finite-dimensional algebras at a levelthat isappropriate for senior undergraduate and first-year graduate students, and (ii) to provide the mathematical foundation needed to prepare the reader for the advanced study of anyone of several fields of mathematics. The subject under study is by no means new-indeed it is classical- yet a book that offers a straightforward and concrete treatment of this theory seems justified for several reasons. First, algebras and linear trans- formations in one guise or another are standard features of various parts of modern mathematics. These include well-entrenched fields such as repre- sentation theory, as well as newer ones such as quantum groups. Second, a study ofthe elementary theory offinite-dimensional algebras is particularly useful in motivating and casting light upon more sophisticated topics such as module theory and operator algebras. Indeed, the reader who acquires a good understanding of the basic theory of algebras is wellpositioned to ap- preciate results in operator algebras, representation theory, and ring theory. In return for their efforts, readers a
Pindex Textbook 2001
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https://doi.org/10.1057/9780230275331that pass through the origin, the only value of . ∈ (0,2.) for which . maps a line back into itself is . = .. In this case, the rotation transformation is particularly simple, for its action on each vector . ∈ ?. is just multiplication by the scalar -1: that is, . = ?. for all . ∈ ?..
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https://doi.org/10.1007/978-3-319-90878-6her than as algebras of linear transformations. The term . generally applies to any algebra of operators that acts on an inner-product space and is closed under the canonical involution, or to any (possibly abstract) C*-algebra.
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